For the function f(x) given in the table, find the average rate of change over each specified interval.
x 0 2 2.5 3 3.8 4 5
f(x) 15 16 20 23 19 17 24
(a) [2, 5]
(b) [3.8, 4]

The inverse of the given function is [tex]f^{-1}(x) = (x-7)^2[/tex].

A function that may reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.

Given that the equation of the function is:

f(x) = √x + 7

Covert the given function into an equation:

y = √x + 7

Interchange the variables in the equation:

x = √y + 7

Isolate the value of y.

Subtract, 7 from both sides of the equation:

x - 7 = √y + 7 - 7

x - 7 = √y

Take square on both sides of the equation:

(x-7)² = (√y)²

(x-7)² = y

Replace, y with [tex]f^{-1}(x)[/tex].

[tex]f^{-1}(x) = (x-7)^2[/tex]

Hence, the inverse of the given function is [tex]f^{-1}(x) = (x-7)^2[/tex].

Learn more about function here:

https://brainly.com/question/2541698

#SPJ1

Based on isosceles trapezoid base angle theorem the sides AD and BC demonstrated that corresponding parts are congruent.

It is a 2-dimensional geometry defined as a quadrilateral with four sides, two of which are parallel to each other.

We provided a trapezoid in which:

BA ≅ CD

It is necessary to demonstrate BD ≅ CD

We can demonstrate this by doing the following:

ABCD is a trapezoidal shape (given)

BA ≅ CD (given) (given)

ABCD is a trapezoid with isosceles angles (definition of isosceles trapezoid)

AD ≅ AD (by using reflexive property) (by using reflexive property)

Angle BAD is congruent to Angle CDA = 5) theorem of base angles

BAD angle CDA angle (base angle theorem)

BD ≅ CA (corresponding parts of congruent triangles are congruent) (corresponding parts of congruent triangles are congruent)

As a result, AD ≅ BC has demonstrated that corresponding parts of congruent triangles are congruent.

To learn more about base angle theorem refer to :

https://brainly.com/question/18779291

#SPJ1

The acceleration of this object is equal to: d) 9.33 m/s^2.

In order to calculate the acceleration of the object, we would apply the second equation of motion. Mathematically, the second equation of motion is given by this mathematical expression:

S = ut + ½at²

Where:  

At time, t = 1.00 seconds, the position is given by:

x₁ = 0 + 1/2(1²)a

x₁ = ¹/₂(a)

At time, t = 2.00 seconds, the position is given by:

x₂ = 0 + 1/2(2²)a

x₂ = 0 + 4a/2

x₂ = 2a

Therefore, the change in position is given by;

Change in position, Δx = x₂ - x₁

Change in position, Δx = 14

From the second equation of motion, the acceleration of this object is given by:

14 = 2a - 1/2(a)

14 = 3a/2

3a = 28

a = 9.33 m/s².

Read more on acceleration here: https://brainly.com/question/13223787

#SPJ1

Complete Question:

An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 14.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?

a) 5.20 m/s^2 b) 10.4 m/s^2 c) 8.67 m/s^2 d) 9.33 m/s^2 e) 12.1 m/s^2

Answer:

0.084

Step-by-step explanation:

                  [tex]\sf Thousandth = \dfrac{1}{1000}\\\\\\[/tex]

[tex]\sf Eighty \ four \ thousandth = 84 * \dfrac{1}{1000}=\dfrac{84}{1000}\\[/tex]

                                   = 0.084

The simplified expression is ab∛ 3ab².

The correct option is (C).

Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.

Given:

2ab (∛192ab²) -5(∛81 [tex]a^4b^5[/tex])

Now, factorizing the terms as

192ab² = 2 x 2 x 2 x 2 x 2 x 2 x 3 x a x b x b

81 [tex]a^4b^5[/tex] = 3 x 3 x 3 x 3 x a x a x a x a x b x b x b x b x b

So, 2ab (∛192ab²) -5(∛81 [tex]a^4b^5[/tex])

= 2ab (∛2 x 2 x 2 x 2 x 2 x 2 x 3 x a x b x b) -5(∛3 x 3 x 3 x 3 x a x a x a x

                                                                                    a x b x b x b x b x b)

= 2ab ( 2 x 2 ∛ 3 x a x b x b) -5( 3 x a x b ∛3 x a x b x b )    

= 8ab ∛ 3ab² - 15ab∛ 3ab²                            

= -7ab ∛ 3ab²

Hence, the simplified expression is ab∛ 3ab².

Learn more about exponent and power here:

https://brainly.com/question/15722035

#SPJ1

Answer:

y- intercept = - 26

Step-by-step explanation:

to find the y- intercept, obtain the equation of the line in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (34, - 52) and (x₂, y₂ ) = (68, - 78) ← 2 ordered pairs from the table

m = [tex]\frac{-78-(-52)}{68-34}[/tex] = [tex]\frac{-78+52}{34}[/tex] = [tex]\frac{-26}{34}[/tex] = - [tex]\frac{13}{17}[/tex] , then

y = - [tex]\frac{13}{17}[/tex] x + c

to find c substitute any of the ordered pairs into the equation and solve for c

using (51, - 65 ) , then

- 65 = - [tex]\frac{13}{17}[/tex] (51) + c = - 39 + c ( add 39 to both sides )

- 26 = c

then y- intercept = - 26

The average cost per​ tape is 10.

The average cost is the ratio of the total of cost of all the products to the total number of products. We can calculate the average cost by dividing the total cost by the total output quantity.

The cost of manufacturing a particular videotape is :

C(x) = 9000+9x

Where

x is the number of tapes produced.

We need to find the value of average per tape i.e.  lim x →9000 C (x)

C (x) = 9000 + 9x

                 x

= 9000   + 9

   x    

Lim n→ 9000 C (x) = 9000    +9

                                 9000

= 1 + 9

= 10

So, the average cost per​ tape is 10

Learn more about average cost here: brainly.com/question/27727800

#SPJ1

The length of midsegment of the trapezoid is MN = 66.5 units

The midsegment of a trapezoid is a line segment that connects the midpoints of the legs of the trapezoid.

The midsegment of a trapezoid is parallel to each base, and its length is one-half the sum of the lengths of the bases.

In this case, length of midsegment of the trapezoid will be:

MN = 1/2 × (76 + 57)

MN = 1/2 × (133)

MN = 66.5 units

Learn more about length of midsegment of a trapezoid on:

brainly.com/question/7593624

#SPJ1

The associated probabilities are A = At least two but no more than five buffers occupied.

There are a total of 2^6 = 64 possible outcomes when rolling 6 dice.

To find the probability of event A, we need to find the number of outcomes where at least two but no more than five buffers are occupied.

This can be done by summing the probabilities of each individual outcome where two, three, four, or five buffers are occupied and subtracting the probabilities where six or zero buffers are occupied.

The probability of two buffers being occupied is (6 choose 2)(1/64) = 15/64

The probability of three buffers being occupied is (6 choose 3)(1/64) = 20/64

The probability of four buffers being occupied is (6 choose 4)(1/64) = 15/64

The probability of five buffers being occupied is (6 choose 5)(1/64) = 6/64

So the probability of event A is (15/64) + (20/64) + (15/64) + (6/64) = 56/64.

B = At least three but no more than five buffers occupied.

To find the probability of event B, we need to find the number of outcomes where at least three but no more than five buffers are occupied.

This can be done by summing the probabilities of each individual outcome where three, four, or five buffers are occupied and subtracting the probability where six buffers are occupied.

The probability of three buffers being occupied is (6 choose 3)(1/64) = 20/64

The probability of four buffers being occupied is (6 choose 4)(1/64) = 15/64

The probability of five buffers being occupied is (6 choose 5)*(1/64) = 6/64

So the probability of event B is (20/64) + (15/64

For more questions like Probability click the link below:

https://brainly.com/question/30034780

#SPJ4

Step-by-step explanation:

g(-4) = 3(-4)-12

= -24

f(g(-4)) = f(-24)

f(-24) = 2(-24)+7

= -41

i don't know it is true i'm just trying:)

Answer: How many cards are in a packet?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Your slope would be -1/4 because it is rise over run meaning your y-axis over your x-axis.  I am not sure exactly what your question is needing but I hope that helps in some way.

Answer:5

Step-by-step explanation:

Comparison of two randomly assigned groups is given by :

a. Given study is classified in experimental based.

b. Treatment group is represented by herb.

c. The independent variable is given by Placebo

d.  The dependent variable represented by the Infection on respiratory tract .

e. Goal of the study is the comparison of two groups herb and the placebo.

Number of randomly assigned group = 2

One group is herb.

Second group is placebo.

a. Two different types of groups given so the study is experimental based.

b. Treatment group is represented by the group one herb.

c. Independent variable is represented by the group two placebo it does not dependent on herb treatment.

d. Dependent variable is represented by the infection on respiratory tract.

e. Goal of the study is given by the comparison of  number of respiratory tract infection in each group.

Therefore, the answer of the following question based on the randomly assigned two groups is given by :

a. Study is experimental based.

b. Herb treatment.

c. Placebo represents the independent variable.

d. Infection represents the dependent variable.

e. Goal of the study is doing the comparison of two groups.

The above question is incomplete, the complete question is :

Subjects were randomly assigned to two groups. One group was given an herb and the other group a placebo. After 6 months the numbers of respiratory tract infections each group had were compared

a) Classify this study (circle the answer): experimental OR observational

b) Identify the treatment group:

c) Identify the independent variable_

d) Identify the dependent variable

e) What is the goal of this study?

learn more about randomly here

brainly.com/question/26125548

#SPJ4

The graphing calculator was used to identify the coordinates of the local extremum point of the polynomial function. This allowed us to find the solution to the word problem by finding the x and y coordinates of the extremum point.

Learn more about Graphing Calculator: https://brainly.com/question/28969437

#SPJ4

Explanation

The ratio 1:2:3 refers to the idea we could have: 1 red, 2 green, 3 blue. The order of the colors is important. Follow the order mentioned in the 1st sentence of the instructions. That order being red:green:blue.

Then the instructions mention that there are actually 5 red (instead of 1 red). This means we multiply each part of the ratio by 5

The ratio 1:2:3 scales up to 5:10:15

We see that there are 15 blue marbles

The assertions relevant for Trade and other receivables are existence, rights and obligations, completeness, and valuation.

Account Assigned: Trade and other receivables

The assertions relevant for Trade and other receivables are existence, rights and obligations, completeness, and valuation.

Existence assertion means that the receivables must exist and they must be recorded in the books of Apple Inc. Rights and obligations assertion means that the receivables must be legally enforceable, and Apple Inc. must have the right to receive the payment from its customers. Completeness assertion means that all the receivables must be recorded in the books of Apple Inc. Valuation assertion means that the receivables must be recorded in Apple Inc.’s financial statements at the correct amount. Valuation can be measured by calculating the amount of receivables as a percentage of total revenue. For example, if the total revenue is $100 million and the total receivables are $20 million, then the receivables are 20% of total revenue.

Learn more about percentage here:

https://brainly.com/question/16797504

#SPJ4

x to the power of z:  2.00^3.00 = 8.00

x to the power of (y to the power of z):  2.00^(4.00^3.00) = 2.00^64.00 = 4096.00

The absolute value of (x minus y):  |2.00 - 4.00| = |-2.00| = 2.00

The square root of (x to the power of z):  √(2.00^3.00) = √8.00 = 4.00

Given three floating-point numbers x, y, and z, the output would be x to the power of z, x to the power of (y to the power of z), the absolute value of (x minus y), and the square root of (x to the power of z). The formula for each output is as follows:

x to the power of z:  x^z

x to the power of (y to the power of z):  x^(y^z)

The absolute value of (x minus y):  |x-y|

The square root of (x to the power of z):  √(x^z)

For example, if x = 2.00, y = 4.00, and z = 3.00, then the output would be:  8.00 4096.00 2.00 4.00

The calculation for each output is as follows:

x to the power of z:  2.00^3.00 = 8.00

x to the power of (y to the power of z):  2.00^(4.00^3.00) = 2.00^64.00 = 4096.00

The absolute value of (x minus y):  |2.00 - 4.00| = |-2.00| = 2.00

The square root of (x to the power of z):  √(2.00^3.00) = √8.00 = 4.00

Learn more about absolute value here :

https://brainly.com/question/1301718

#SPJ4

The probability that she will make a basket on or before her last attempt within her average waiting time are 1/8 and 2/8

Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment.

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.

Given;

Hannah makes 5 out of 8 attempted free-throws

Now,

The average waiting time of hannah to make her first basket=5/8

The probability of hannah making basket at her last attempt=1/8

The probability of hannah making basket before her last attempt= 2/8

Therefore, the probabilty will be 1/8 and 2/8.

Learn more about interpretation of probability here:

https://brainly.com/question/23024246

#SPJ1

Answer: x= -3 and x= -1

Step-by-step explanation:

We can see from table that when x= -3, the f(x) have the same y with g(x). Also when x= -1, the f(x) have the same y with g(x).

Answer:

  (x, y) = (2, 5)

Step-by-step explanation:

You want to solve the system of equations ...

Substituting for y, we have ...

  x = 12 -2(2x +1)

  x = 12 -4x -2 . . . . . eliminate parentheses

  5x = 10 . . . . . . add 4x

  x = 2 . . . . . . divide by 5

Then the value of y is ...

  y = 2(2) +1 = 5

The solution is ...

<95141404393>

The third girl will recieve a land area equals to the fraction  (2y-x)/2y.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

The three main sorts of fractions are as follows. Proper fractions, improper fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.

The fractions are x/3y, x/6y and z(say)

so sum of all the fraction must be 1 so

x/3y + x/6y + z = 1

⇒z = (2y-x)/2y

The third girl recieve a land area equals to (2y-x)/2y.

To learn more about Fraction refer to :

https://brainly.com/question/3685292

#SPJ1

All real numbers, with the exception of -6 , are the solution to a rational equation. The quotient of two polynomials is the definition of a rational expression.

[tex]$\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7} \quad: \quad x \neq-6$[/tex]

[tex]$\frac{(x-2)(x+6)}{7(x+6)}=\frac{x-2}{7}$[/tex]

Simplify

[tex]$\frac{(x-2)(x+6)}{7(x+6)}: \quad \frac{x-2}{7}$[/tex]

[tex]$\frac{x-2}{7}=\frac{x-2}{7}$[/tex]

Seven times both sides

[tex]$\frac{x-2}{7} \cdot 7=\frac{x-2}{7} \cdot 7$[/tex]

Simplify

[tex]$x-2=x-2$[/tex]

There is equality between the two sides.

For every x Verify Solutions, true

Search for ill-defined (singularity) points: [tex]$x=-6$[/tex]

Because -6, the equation is undefined.

[tex]x \neq -6[/tex]

Therefore the correct answer is option C ) All real numbers except -6 .

To learn more about rational expression refer to :

https://brainly.com/question/30291585

#SPJ1

Answer:

-4/5 OR -0.8

Step-by-step explanation:

This problem is very simple but it can be broken down

First we do -3 times 8 and get -24

Then we do 5 times 6 and get 30

We put the first answer over the second which equals

-24/30

This can then be simplified further if we divide both sides by 6

-4/5 as a fraction

-0.8 as a decimal

-80% as a percent

Answer:

Slope = 4/3

Step-by-step explanation:

The coordinates are,

→ x1 = 6, y1 = 0

→ x2 = 0, y2 = -8

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Now required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (-8 - 0)/(0 - 6)

→ m = (-8)/(-6)

→ m = 8/6

→ [ m = 4/3 ]

Hence, the slope is 4/3.

here is ur answer seeee now

The parametric vector represents a line, whose slope and intercept are 12 and - 35, respectively.

Parametric functions are multi-dimensional functions in terms of a variable t that is a real number. In this problem we find a parametric function with coordinates, that is, a vector of the form (x, y) = (f(t), g(x)) and we are supossed to determine the rectangular form of such function, that is, a function of the form:

y = f(x)

The rectangular form of the function is a line if and only if the resulting expression is of the form:

y = m · x + b

Where:

First, write the components of the parametric functions:

x = 2 · t + 3

y = 24 · t + 1

Second, clear variable t in each parametric expression:

t = (x - 3) / 2

t = (y - 1) / 24

Third, eliminate parameter t by transitive property:

(x - 3) / 2 = (y - 1) / 24

Fourth, obtain the equation of the line:

24 · (x - 3) = 2 · (y - 1)

24 · x - 72 = 2 · y - 2

24 · x - 70 =  2 · y

y = 12 · x - 35

Fifth, determine the slope and intercept of the equation of the line:

m = 12, b = - 35

To learn more on parametric functions: https://brainly.com/question/23725782

#SPJ1

The range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2.

The range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2 can be calculated using the following formula:

Range = Maximum Value - Minimum Value

The expression inside the parentheses can be simplified to 3cos2a cos4a + 3sin2a sin4a and the expression inside the exponential can be simplified to tan2a (1 / cos2a - sin2a). This gives us the expression

Range = 3cos2a cos4a + 3sin2a sin4a ^ tan2a (1 / cos2a - sin2a)

To calculate the maximum and minimum values, we can use derivatives to find the critical points of the expression. Taking the first derivative with respect to a, we get

d/da (3cos2a cos4a + 3sin2a sin4a ^ tan2a (1 / cos2a - sin2a)) = 0

Solving this equation gives us the critical points of a = ±7t/6. Using these values, we can calculate the maximum and minimum values of the expression.

Maximum Value = 3cos14t/6 cos8t/6 + 3sin14t/6 sin8t/6 ^ tan4t/3 (1 / cos14t/6 - sin14t/6)

Minimum Value = 3cos22t/6 cos16t/6 + 3sin22t/6 sin16t/6 ^ tan4t/3 (1 / cos22t/6 - sin22t/6)

Finally, using the formula for the range, we can calculate the range of the expression to be

Range = 3cos14t/6 cos8t/6 + 3sin14t/6 sin8t/6 ^ tan4t/3 (1 / cos14t/6 - sin14t/6) - (3cos22t/6 cos16t/6 + 3sin22t/6 sin16t/6 ^ tan4t/3 (1 / cos22t/6 - sin22t/6))

This expression gives us the range of sina(3cos2a cos4a 3sin2a sin2a cos2a) ^ tan a(sec a -sina tana) where a is not an integer multiple of 7t/2.

Learn more about Range here:

https://brainly.com/question/16664109

#SPJ4

There are a total of 6 homework assignments that need to be completed one night. The number of ways to arrange n items in a specific order is n! (n factorial).

Therefore, for 6 homework assignments, the number of different orders in which they can be completed is 6! = 720.

This means that there are 720 different ways in which you can complete these 6 assignments on one night. Each permutation represents a unique order in which the assignments can be completed, such as starting with assignment 1, then 2, then 3, and so on, or starting with assignment 4, then 5, then 6, and then 1, and so on.

It is worth noting that this formula is only applicable when the order of the assignments matters. If the order of the assignments does not matter, then we would use the formula for combinations, which is n! / (r!(n-r)!).

Multiplying all of these options together results in 6 x 5 x 4 x 3 x 2 x 1 = 720 possible ways to complete the assignments in a different order. This is known as the permutation formula, which states that the number of ways to arrange n items in a specific order is n! (n factorial).

To learn more about homework assignments refer to;

brainly.com/question/26489013

#SPJ1

Answer:

please take a better picture

Step-by-step explanation: